dsbgvd(3P) Sun Performance Library dsbgvd(3P)NAMEdsbgvd - compute all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of the
form A*x=(lambda)*B*x
SYNOPSIS
SUBROUTINE DSBGVD(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
LDZ, WORK, LWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER N, KA, KB, LDAB, LDBB, LDZ, LWORK, LIWORK, INFO
INTEGER IWORK(*)
DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE DSBGVD_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
LDZ, WORK, LWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, LWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE SBGVD(JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], W,
Z, [LDZ], [WORK], [LWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, LWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: AB, BB, Z
SUBROUTINE SBGVD_64(JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB],
W, Z, [LDZ], [WORK], [LWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, LWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: AB, BB, Z
C INTERFACE
#include <sunperf.h>
void dsbgvd(char jobz, char uplo, int n, int ka, int kb, double *ab,
int ldab, double *bb, int ldbb, double *w, double *z, int
ldz, int *info);
void dsbgvd_64(char jobz, char uplo, long n, long ka, long kb, double
*ab, long ldab, double *bb, long ldbb, double *w, double *z,
long ldz, long *info);
PURPOSEdsbgvd computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of the
form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and
banded, and B is also positive definite. If eigenvectors are desired,
it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard digit
in add/subtract, or on those binary machines without guard digits which
subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
conceivably fail on hexadecimal or decimal machines without guard dig‐
its, but we know of none.
ARGUMENTS
JOBZ (input)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input)
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) The order of the matrices A and B. N >= 0.
KA (input)
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KA >= 0.
KB (input)
The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KB >= 0.
AB (input/output)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first ka+1 rows of the array. The j-
th column of A is stored in the j-th column of the array AB
as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for
max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
j<=i<=min(n,j+ka).
On exit, the contents of AB are destroyed.
LDAB (input)
The leading dimension of the array AB. LDAB >= KA+1.
BB (input/output)
On entry, the upper or lower triangle of the symmetric band
matrix B, stored in the first kb+1 rows of the array. The j-
th column of B is stored in the j-th column of the array BB
as follows: if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for
max(1,j-kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for
j<=i<=min(n,j+kb).
On exit, the factor S from the split Cholesky factorization B
= S**T*S, as returned by DPBSTF.
LDBB (input)
The leading dimension of the array BB. LDBB >= KB+1.
W (output)
If INFO = 0, the eigenvalues in ascending order.
Z (output)
If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
eigenvectors, with the i-th column of Z holding the eigenvec‐
tor associated with W(i). The eigenvectors are normalized so
Z**T*B*Z = I. If JOBZ = 'N', then Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ
= 'V', LDZ >= max(1,N).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension of the array WORK. If N <= 1,
LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= 3*N. If JOBZ
= 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
IWORK (workspace/output)
On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input)
The dimension of the array IWORK. If JOBZ = 'N' or N <= 1,
LIWORK >= 1. If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the rou‐
tine only calculates the optimal size of the IWORK array,
returns this value as the first entry of the IWORK array, and
no error message related to LIWORK is issued by XERBLA.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is:
<= N: the algorithm failed to converge: i off-diagonal ele‐
ments of an intermediate tridiagonal form did not converge to
zero; > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF
returned INFO = i: B is not positive definite. The factor‐
ization of B could not be completed and no eigenvalues or
eigenvectors were computed.
FURTHER DETAILS
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
6 Mar 2009 dsbgvd(3P)
